scholarly journals Analysis of Forward Model, Data Type, and Prior Information in Probabilistic Inversion of Crosshole GPR Data

2021 ◽  
Vol 13 (2) ◽  
pp. 215
Author(s):  
Hui Qin ◽  
Zhengzheng Wang ◽  
Yu Tang ◽  
Tiesuo Geng
Keyword(s):  
Posterior Distribution ◽  
Relative Permittivity ◽  
Prior Distribution ◽  
Prior Information ◽  
Data Type ◽  
Forward Model ◽  
Model Parameters ◽  
Model Data ◽  
Waveform Data ◽  
First Arrival

The crosshole ground penetrating radar (GPR) is a widely used tool to map subsurface properties, and inversion methods are used to derive electrical parameters from crosshole GPR data. In this paper, a probabilistic inversion algorithm that uses Markov chain Monte Carlo (MCMC) simulations within the Bayesian framework is implemented to infer the posterior distribution of the relative permittivity of the subsurface medium. Close attention is paid to the critical elements of this method, including the forward model, data type and prior information, and their influence on the inversion results are investigated. First, a uniform prior distribution is used to reflect the lack of prior knowledge of model parameters, and inversions are performed using the straight-ray model with first-arrival traveltime data, the finite-difference time-domain (FDTD) model with first-arrival traveltime data, and the FDTD model with waveform data, respectively. The cases using first-arrival traveltime data require an unreasonable number of model evaluations to converge, yet are not able to recover the real relative permittivity field. In contrast, the inversion using the FDTD model with waveform data successfully infers the correct model parameters. Then, the smooth constraint of model parameters is employed as the prior distribution. The inversion results demonstrate that the prior information barely affects the inversion results using the FDTD model with waveform data, but significantly improves the inversion results using first-arrival traveltime data by decreasing the computing time and reducing uncertainties of the posterior distribution of model parameters.

Multimodal Markov chain Monte Carlo method for nonlinear petrophysical seismic inversion

Geophysics ◽  
2019 ◽  
Vol 84 (5) ◽  
pp. M1-M13 ◽  
Author(s):  
Leandro Passos de Figueiredo ◽  
Dario Grana ◽  
Mauro Roisenberg ◽  
Bruno B. Rodrigues
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Posterior Distribution ◽  
Seismic Inversion ◽  
Forward Model ◽  
Model Parameters ◽  
Petrophysical Properties ◽  
Mcmc Method ◽  
Data Set

One of the main objectives in the reservoir characterization is estimating the rock properties based on seismic measurements. We have developed a stochastic sampling method for the joint prediction of facies and petrophysical properties, assuming a nonparametric mixture prior distribution and a nonlinear forward model. The proposed methodology is based on a Markov chain Monte Carlo (MCMC) method specifically designed for multimodal distributions for nonlinear problems. The vector of model parameters includes the facies sequence along the seismic trace as well as the continuous petrophysical properties, such as porosity, mineral fractions, and fluid saturations. At each location, the distribution of petrophysical properties is assumed to be multimodal and nonparametric with as many modes as the number of facies; therefore, along the seismic trace, the distribution is multimodal with the number of modes being equal to the number of facies power the number of samples. Because of the nonlinear forward model, the large number of modes and as a consequence the large dimension of the model space, the analytical computation of the full posterior distribution is not feasible. We then numerically evaluate the posterior distribution by using an MCMC method in which we iteratively sample the facies, by moving from one mode to another, and the petrophysical properties, by sampling within the same mode. The method is extended to multiple seismic traces by applying a first-order Markov chain that accounts for the lateral continuity of the model properties. We first validate the method using a synthetic 2D reservoir model and then we apply the method to a real data set acquired in a carbonate field.

The Research on Share Rate of Trip Mode Choice Based on Bayesian Theory

2013 ◽  
Vol 373-375 ◽  
pp. 2262-2265
Author(s):  
Yong Liao ◽  
Tao Wu
Keyword(s):  
Posterior Distribution ◽  
Logit Model ◽  
Prior Distribution ◽  
Conditional Distribution ◽  
Prior Information ◽  
Mode Choice ◽  
Forecast Accuracy ◽  
Total Probability ◽  
Parameter Calibration ◽  
Bayes Analysis

Based on Bayes analysis, a new model of trip mode choice is presented. Trip mode choice is divided into three phases: calculating prior distribution, obtaining conditional distribution by sampling and calculating share rate of trip modes. Supply characteristics of trip modes are taken as prior information. Unity value takes the place of unity function in MNL, and then prior distribution is achieved. Condition distribution is gained from sampling information. Bayes analysis is introduced into calculating posterior distribution. Share rates of trip modes, is calculated by total probability formula. Compared with other choice models, Model proposed in this paper improves the forecast accuracy of share rate without the need of parameter calibration like Logit model.

Model of the influence of Internet finance on monetary policy based on gibbs sampling and vector autoregression

2020 ◽  
pp. 1-11
Author(s):  
Hui Wang ◽  
Huang Shiwang
Keyword(s):  
Monetary Policy ◽  
Gibbs Sampling ◽  
Posterior Distribution ◽  
Estimation Method ◽  
Financial Supervision ◽  
Var Model ◽  
Model Parameters ◽  
State Variables ◽  
Frequency Data ◽  
Internet Finance

The various parts of the traditional financial supervision and management system can no longer meet the current needs, and further improvement is urgently needed. In this paper, the low-frequency data is regarded as the missing of the high-frequency data, and the mixed frequency VAR model is adopted. In order to overcome the problems caused by too many parameters of the VAR model, this paper adopts the Bayesian estimation method based on the Minnesota prior to obtain the posterior distribution of each parameter of the VAR model. Moreover, this paper uses methods based on Kalman filtering and Kalman smoothing to obtain the posterior distribution of latent state variables. Then, according to the posterior distribution of the VAR model parameters and the posterior distribution of the latent state variables, this paper uses the Gibbs sampling method to obtain the mixed Bayes vector autoregressive model and the estimation of the state variables. Finally, this article studies the influence of Internet finance on monetary policy with examples. The research results show that the method proposed in this article has a certain effect.

scholarly journals Sequential modelling of the Earth’s core magnetic field

2020 ◽  
Vol 72 (1) ◽  
Author(s):  
Guillaume Ropp ◽  
Vincent Lesur ◽  
Julien Baerenzung ◽  
Matthias Holschneider
Keyword(s):  
Magnetic Field ◽  
Prior Information ◽  
Spatial Scales ◽  
Model Parameters ◽  
International Geomagnetic Reference Field ◽  
The Earth ◽  
Temporal And Spatial ◽  
Different Sources ◽  
Original Approach ◽  
Modelling Approach

Abstract We describe a new, original approach to the modelling of the Earth’s magnetic field. The overall objective of this study is to reliably render fast variations of the core field and its secular variation. This method combines a sequential modelling approach, a Kalman filter, and a correlation-based modelling step. Sources that most significantly contribute to the field measured at the surface of the Earth are modelled. Their separation is based on strong prior information on their spatial and temporal behaviours. We obtain a time series of model distributions which display behaviours similar to those of recent models based on more classic approaches, particularly at large temporal and spatial scales. Interesting new features and periodicities are visible in our models at smaller time and spatial scales. An important aspect of our method is to yield reliable error bars for all model parameters. These errors, however, are only as reliable as the description of the different sources and the prior information used are realistic. Finally, we used a slightly different version of our method to produce candidate models for the thirteenth edition of the International Geomagnetic Reference Field.

A Comparison of Approaches to Select the Informativeness of Priors in BVARs

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Jan Prüser ◽  
Christoph Hanck
Keyword(s):  
Impulse Response ◽  
Prior Information ◽  
Hierarchical Modeling ◽  
Small Samples ◽  
Model Parameters ◽  
Impulse Response Functions ◽  
Response Functions ◽  
Vector Autoregressions ◽  
The Rich ◽  
Bayesian Vars

Abstract Vector autoregressions (VARs) are richly parameterized time series models that can capture complex dynamic interrelationships among macroeconomic variables. However, in small samples the rich parametrization of VAR models may come at the cost of overfitting the data, possibly leading to imprecise inference for key quantities of interest such as impulse response functions (IRFs). Bayesian VARs (BVARs) can use prior information to shrink the model parameters, potentially avoiding such overfitting. We provide a simulation study to compare, in terms of the frequentist properties of the estimates of the IRFs, useful strategies to select the informativeness of the prior. The study reveals that prior information may help to obtain more precise estimates of impulse response functions than classical OLS-estimated VARs and more accurate coverage rates of error bands in small samples. Strategies based on selecting the prior hyperparameters of the BVAR building on empirical or hierarchical modeling perform particularly well.

scholarly journals Measurement of technical efficiency in the case of heterogeneity of technologies used between firms – Based on evidence from Polish crop farms

2021 ◽  
Author(s):  
Jerzy Marzec ◽  
Andrzej Pisulewski
Keyword(s):  
Technical Efficiency ◽  
Production Function ◽  
Prior Distribution ◽  
Prior Information ◽  
Stochastic Frontier ◽  
Returns To Scale ◽  
Random Coefficients ◽  
Point Of View ◽  
Model Specification ◽  
Stochastic Frontier Models

In the present study, we have investigated several competing stochastic frontier models which differ in terms of the form of the production function (Cobb-Douglas or translog), inefficiency distribution (half-normal or exponential distribution) and type of prior distribution for the parameters (hierarchical or non-hierarchical from the Bayesian point of view). This last distinction corresponds to a difference between random coefficients and fixed coefficients models. Consequently, this study aims to examine to what extent inferences about estimates of farms' efficiency depend on the above assumptions. Moreover, the study intends to investigate how far the production function's characteristics are affected by the choice of the type of prior distribution for the parameters. First of all, it was found that the form of the production function does not impact the efficiency scores. Secondly, we found that measures of technical efficiency are sensitive to distributional assumptions about the inefficiency term. Finally, we have revealed that estimates of technical efficiency are reasonably robust to the prior information about the parameters of crop farms' production technology. There is also a resemblance in the elasticity of output with respect to inputs between the models considered in this paper. Additionally, the measurement of returns to scale is not sensitive to model specification.

scholarly journals An In-Class Demonstration of Bayesian Inference

2019 ◽  
Author(s):  
Johnny van Doorn ◽  
Dora Matzke ◽  
Eric-Jan Wagenmakers
Keyword(s):  
Bayesian Inference ◽  
Posterior Distribution ◽  
Prior Distribution ◽  
Sequential Analysis ◽  
Bayes Factor ◽  
Classroom Setting ◽  
Key Concepts

Sir Ronald Fisher's venerable experiment "The Lady Tasting Tea'' is revisited from a Bayesian perspective. We demonstrate how a similar tasting experiment, conducted in a classroom setting, can familiarize students with several key concepts of Bayesian inference, such as the prior distribution, the posterior distribution, the Bayes factor, and sequential analysis.

Bayesian Comparison of Two Regression Lines

1978 ◽  
Vol 3 (2) ◽  
pp. 179-188
Author(s):  
Robert K. Tsutakawa
Keyword(s):  
Posterior Distribution ◽  
Prior Distribution ◽  
Posterior Probability ◽  
Finite Interval ◽  
Regression Line ◽  
The Other ◽  
End Points ◽  
Independent Variable

The comparison of two regression lines is often meaningful or of interest over a finite interval I of the independent variable. When the prior distribution of the parameters is a natural conjugate, the posterior distribution of the distances between two regression lines at the end points of I is bivariate t. The posterior probability that one regression line lies above the other uniformly over I is numerically evaluated using this distribution.

Metropolis-Hastings Algorithms for DSGE Models

2015 ◽  
Author(s):  
Edward P. Herbst ◽  
Frank Schorfheide
Keyword(s):  
Random Walk ◽  
Posterior Distribution ◽  
Prior Distribution ◽  
Large Scale ◽  
Likelihood Function ◽  
Dsge Models ◽  
Posterior Distributions ◽  
Dsge Model ◽  
Alternative Proposal ◽  
Posterior Moments

This chapter talks about the most widely used method to generate draws from posterior distributions of a DSGE model: the random walk MH (RWMH) algorithm. The DSGE model likelihood function in combination with the prior distribution leads to a posterior distribution that has a fairly regular elliptical shape. In turn, the draws from a simple RWMH algorithm can be used to obtain an accurate numerical approximation of posterior moments. However, in many other applications, particularly those involving medium- and large-scale DSGE models, the posterior distributions could be very non-elliptical. Irregularly shaped posterior distributions are often caused by identification problems or misspecification. In lieu of the difficulties caused by irregularly shaped posterior surfaces, the chapter reviews various alternative MH samplers, which use alternative proposal distributions.

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